Download EXTRA PRACTICE, Sections 7.3 and 7.4

Bittinger/Ellenbogen, Intermediate Algebra: Concepts and Applications, 6E
EXTRA PRACTICE, Sections 7.3 and 7.4
Name_______________________________
Multiplying, Dividing, and Simplifying Radical Expressions
______________________________________________________________________________
Examples. Simplify. Assume that all variables represent positive numbers.
a)
4
(81a 8b 4 ) 2
= 3 64 ⋅ 5 ⋅ x 6 ⋅ y 3 ⋅ y ⋅ z 2
=
(
= 64 x y
= ( 3a b)
3
320 x 6 y 4 z 2
6
3
33
b)
5 yz
= 4 x 2 y 3 5 yz 2
2
4
34 a 8 b 4
2
75 y 5
16 x 2
c)
)
2
=
2
=
75 y 5
16 x 2
25 y 4 ⋅ 3 y
16 x 2
5y 2 3y
=
4x
= 9a 4 b 2
Simplify. Assume that all variables represent positive numbers.
20 x 3 yz 2 = ____________________
2.
a 16b 12 = ______________________
4.
49a 3
= ______________________
b4
45a 3bc 2 = ____________________
6.
16 3 = ________________________
16 x 5
= _______________________
y6
8.
4
64a 7 b 12 = ____________________
9.
50a 2 b 5 = ______________________
10.
5
(32 x 10 ) 3
11.
16 x 3
= _______________________
81
12.
1.
3.
4
5.
7.
3
500 x 2 yz 11 = __________________
14.
240 x 4 y 5 = ____________________
16.
4
x 7 y 9 z 12 = ____________________
24 x 3
= _____________________
25
18.
4
256 3 = _______________________
(32a 5b10 ) 3
20.
3
(54a 3 ) 2
216 = _______________________
15.
3
5
= ____________________
64a 7
= ______________________
27
13.
19.
128 x 4 y 2 = ____________________
3
3
17.
3
2
= ___________________
Copyright © 2002 Pearson Education, Inc.
= ____________________
Bittinger/Ellenbogen, Intermediate Algebra: Concepts and Applications, 6E
EXTRA PRACTICE, Sections 7.3 and 7.4 (cont.)
Multiplying, Dividing, and Simplifying Radical Expressions
______________________________________________________________________________
Examples. Assume that all variables represent positive numbers.
a)
Multiply and simplify.
b)
32 xy 3 4 x 2 y 5
= 128 x y
3
Divide and simplify.
3
56a 5b 14
3
=
8
7ab 5
56a 5b 14
7ab 5
3
= 64 ⋅ 2 ⋅ x 2 ⋅ x ⋅ y 8
= 64 x 2 y 8 2 x
= 3 8a 4 b 9
= 8 xy 4 2 x
= 3 8 ⋅ a 3 ⋅ a ⋅ b 9 = 2ab 3 3 a
Multiply or divide and simplify. Assume that all variables represent positive numbers.
21.
3
5( x + 2)
25( x + 2) =
2 3
2
32a 5b 3
22.
=
2ab 2
_______________
23.
6 45x 3
=
3 5x
8 x 3 y 3xy 2 =
25.
3
27.
29.
31.
3
625x 6 y 4
3
5xy
5
2
6 a b
3
=
6 ab =
2
95 160 x 8 y 11
35 5xy
2
=
__________________
_______________
24.
_______________
26.
_______________
28.
3
x 7 3 64 xy 2 = __________________
3
81a 5b 8
6( x + 3)
3
_______________
30.
_______________
32.
=
3ab 2
3
27 xy 7
3
3
xy
3( x + 3) = ____________
3
=
4( y − 3)
2
__________________
__________________
3
2( y − 3) =
5
__________________
Copyright © 2002 Pearson Education, Inc.
Bittinger/Ellenbogen, Intermediate Algebra: Concepts and Applications, 6E
EXTRA PRACTICE ANSWERS, Sections 7.3 and 7.4
1. 2 xz 5xy
12. 10 xz 5 5 yz
23. 6x
2. 4 x 3 2 xy 2
13. 36
24. 4 x 2 3 x 2 y 2
3. a 4 b 3
14.
4a 2 3 a
3
25. 2 x 2 y 6 y
26. 3ab 2 3 a
7a a
4.
b2
15. 2 xy 3 30 xy
5. 3ac 5ab
16. xy 2 z 3 4 x 3 y
6. 64
3
7.
2x 2x
y2
2
17.
2
2 x 6x
5
18. 64
27. 5xy 3 x 2
2
28. 3( x + 3) 2
29. 36a 3 6b 2
30. 3 y 2
8. 2ab 3 4 4a 3
19. 8a 3b 6
31. 6 xy 5 x 2 y 4
9. 5ab 2 2b
20. 9a 2 3 4
32. 2( y − 3)
10. 8 x 6
21. 5( x + 2) 3 x + 2
4x x
11.
9
22. 4a 2 b
Copyright © 2002 Pearson Education, Inc.
2
3
y−3